An implementation of the reconstruction algorithm of A Nachman for the 2D inverse conductivity problem

By Samuli Siltanen, Jennifer L. Mueller, D. Isaacson. 2000

212 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Electrical and Electronic Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e5015da5f2af9487451d1e3e6cf3ff70f4ed6435

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In Biomedical Engineering

In Electrical and Electronic Engineering

In Mathematical Physics

Citations in the corpus

Carleman estimates for global uniqueness, stability and numerical methods for coefficient inverse problems (2012, methodology): “[141] S. Siltanen, J. Mueller and D. Isaacson, An implementation of the reconstruction algorithm of A. Nachman for the 2-”
Electrical impedance tomography (2002, methodology): “In two dimensions, the injectivity of the dc map σ is established by Nachman [118], in a constructive proof which has been implemented in [134].”
Numerical solution method for the dbar-equation in the plane (2004, methodology): “[34] for EIT in the numerical algorithm based on Nachman s uniqueness proof for the 2-D inverse conductivity problem [26].”
REGULARIZED D-BAR METHOD FOR THE INVERSE CONDUCTIVITY PROBLEM (2009, methodology): “Finally, we present a couple of reconstructions using the Born approximation as was done in [82, 68, 67, 41, 42, 53, 52].”
Calderon's inverse conductivity problem in the plane (2006, background): “For the numerical implementation of [22] see [27].”
On the continuum limit of a discrete inverse spectral problem on optimal finite difference grids (2005, background): “The extension to two-dimensional problems seems especially promising due to recent results for planar graphs [22, 46, 48] and the ∂-bar approach [53, 65, 74] that can be considered as two-dimensional counterparts of the Stieltjes and Gel′fand-Levitan methods, respectively.”
Recent advances in diffuse optical imaging (2005, methodology): “Inclusion of such anatomical details has been shown to improve the quality of reconstructed images in EIT (Bagshaw et al 2003), although generating the 3D finite element mesh was difficult and timeconsuming (Bayford et al 2001, Lionheart 2004).”